In the last years, the need for enhancing health and preventing problems with remote monitoring is increasing. A non-invasive low-cost technique for processing bio-signals and monitoring vital parameters, at rest and during physical activity, is the use of wearable PhotoPlethysmoGraphic (PPG) systems. However, in order to detect a relevant vital parameter, such as the heart rate during demanding exercises, motion artifacts must be removed from the signals retrieved. In this paper, we present a fast and easy to implement algorithm to estimate the heart rate value which does not need to reconstruct the noise-free signal nor does it apply adaptive filtering as existing algorithms, thus gaining computational time and stored memory space. The method consists of applying the Fast Fourier Transform on short windows of data and removing motion artifacts relying on single-sided amplitude spectrum analysis of PPG and 3-axis accelerometer signals. The results show that our algorithm manages to remove a wide range of motion artifacts achieving an average absolute error of only 1.27 BPM between the heart rate estimated by the algorithm every second and the ground-truth value. The method was successfully implemented on a wearable PPG device achieving an execution time of 226 ms per second, hence obtaining a battery lifetime of 9.37 days.